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# Two women, A and B working separately can mow a field in 8

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Two women, A and B working separately can mow a field in 8 [#permalink]

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28 Jun 2010, 09:01
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Two women, A and B working separately can mow a field in 8 and 12 hrs respectively. If they work together in stretches on 1 hr alternately, A beginning at 9:00 AM, when will the mowing be finished?

Can anybody plz explain the best way to solve such problems?
[Reveal] Spoiler: OA

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28 Jun 2010, 09:34
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Two women, A and B working separately can mow a field in 8 and 12 hrs respectively. If they work together in stretches on 1 hr alternately, A beginning at 9:00 AM, when will the mowing be finished?

Can anybody plz explain the best way to solve such problems?

In 1 hour A does $$\frac{1}{8}=\frac{3}{24}$$th of the whole job and B $$\frac{1}{12}=\frac{2}{24}$$th of the whole job (common denimnator makes the following calculations easier). So in 2 hours they do $$\frac{3}{24}+\frac{2}{24}=\frac{5}{24}$$th of the whole job (so at this stage we know that time needed to do the whole job will be less than 5 2-hour periods or 10 hours, as $$5*\frac{5}{24}=\frac{25}{24}>1$$).

Now in 8 hours (4 two hour periods) they do $$4*\frac{5}{24}=\frac{20}{24}$$th of the whole job. Then will be A's turn and by the end of 9 hours $$\frac{20}{24}+\frac{3}{24}=\frac{23}{24}$$th of the job will be done and $$\frac{1}{24}$$th will be left, which can be done by B (as it's B's turn now) in 1/2hours (30 minutes). So total time $$8+1+\frac{1}{2}=9\frac{1}{2}$$, hence they will finish at $$9:00AM+9\frac{1}{2}=18:30PM$$.

Similar problem: pipes-and-cisterns-93482.html#p719223

Hope it's clear.
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28 Jun 2010, 10:17
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Thanks Bunuel for the detailed solution, can u pls advise why we calculated for 2 hrs?

2 hours is 1 cycle - a period of time when both A and B worked once. As long as we know what part of the job is done in one cycle we can find in which range to look for the correct answer. We had that the period of time must be less than 5 cycles (10 hours) and then we started calculating directly for 4 cycles, which saved us some time.
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28 Jun 2010, 10:30
dont use the algebric way on this one. just draw a table and add the values: a=3/24 an b=2/24.
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28 Jun 2010, 10:34
Bunuel wrote:
Thanks Bunuel for the detailed solution, can u pls advise why we calculated for 2 hrs?

2 hours is 1 cycle - a period of time when both A and B worked once. As long as we know what part of the job is done in one cycle we can find in which range to look for the correct answer. We had that the period of time must be less than 5 cycles (10 hours) and then we started calculating directly for 4 cycles, which saved us some time.

Thanks Bunuel, One more question my understanding for "If they work together in stretches on 1 hr alternately," sentence was, they will work alternatively lets say A will work at 9:00 AM and B will start at 10:00AM. If my understanding is correct the how come 9th hr will come for A?
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28 Jun 2010, 10:36
mikioso wrote:
dont use the algebric way on this one. just draw a table and add the values: a=3/24 an b=2/24.

It will be helpful Mikioso, if u can explain that method.
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28 Jun 2010, 10:37

Thanks Bunuel, One more question my understanding for "If they work together in stretches on 1 hr alternately," sentence was, they will work alternatively lets say A will work at 9:00 AM and B will start at 10:00AM. If my understanding is correct the how come 9th hr will come for A?

Hi,

A goes first, so A does the 1st hour, 3rd hour, 5th hour, 7th hour, 9th hour, ...
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28 Jun 2010, 10:40
skovinsky wrote:

Thanks Bunuel, One more question my understanding for "If they work together in stretches on 1 hr alternately," sentence was, they will work alternatively lets say A will work at 9:00 AM and B will start at 10:00AM. If my understanding is correct the how come 9th hr will come for A?

Hi,

A goes first, so A does the 1st hour, 3rd hour, 5th hour, 7th hour, 9th hour, ...

Thanks skovinsky, now I got it
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30 Jun 2010, 10:00
mmm... the working alternately thing is kind of a pain.

So in the first hour A did 1/8th of the job, & in the 2nd hour B did 1/12th of the job. In 2 hours, they did 5/24 of the job together. Meaning in 8 hours they would have completed (5/24)X4=20/24.

In the 9th hour, A is on shift again & completes 1/8th (or in other words, 3/24th) of the job, so we're now that 23/24. In the 10th hour, B completes the remainder 1/24th. We know B can do 1/12th in 1 hour, so she'll only take half the hour to complete 1/24th of the job.

We do some counting with our fingers & see that it takes 9.5 hours. So starting at 0900 (9am in civilian time), we would complete the job at 18:30 or 6:30pm.

Kind of a pain in the ass but doable in 2 minutes.
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Re: Two women, A and B working separately can mow a field in 8 [#permalink]

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28 Jul 2013, 01:46
Two women, A and B working separately can mow a field in 8 and 12 hrs respectively. If they work together in stretches on 1 hr alternately, A beginning at 9:00 AM, when will the mowing be finished?

HI Bunnel
Please clarify me where I have gone wrong

Rate A-1/8
Rate B-1/12

let say A works for 4 hour and rate is 1/8 so total job done = 1/8*4=1/2
Similarly let say B works for 6 hour and rate is 1/12 so total job done=1/12*6=1/2

So both can finish the work in 10 hours if they work alternatively. 9.00 am+10 hour=19.00pm answer

Where i have gone wrong..............

Rgds
Prasannajeet
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Re: Two women, A and B working separately can mow a field in 8 [#permalink]

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28 Jul 2013, 05:01
Expert's post
prasannajeet wrote:
Two women, A and B working separately can mow a field in 8 and 12 hrs respectively. If they work together in stretches on 1 hr alternately, A beginning at 9:00 AM, when will the mowing be finished?

HI Bunnel
Please clarify me where I have gone wrong

Rate A-1/8
Rate B-1/12

let say A works for 4 hour and rate is 1/8 so total job done = 1/8*4=1/2
Similarly let say B works for 6 hour and rate is 1/12 so total job done=1/12*6=1/2

So both can finish the work in 10 hours if they work alternatively. 9.00 am+10 hour=19.00pm answer

Where i have gone wrong..............

Rgds
Prasannajeet

I think you misinterpreted the question. A and B work in shifts: A goes first and works for 1 hour, then goes B and works for 1 hour, ... Thus, for this scenario it's not possible A to work 4 hours and B 6 hours.
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Re: Two women, A and B working separately can mow a field in 8 [#permalink]

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10 Aug 2014, 07:53
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Re: Two women, A and B working separately can mow a field in 8 [#permalink]

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12 Oct 2015, 09:42
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Re: Two women, A and B working separately can mow a field in 8 [#permalink]

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09 Nov 2015, 14:37
Bunuel wrote:
prasannajeet wrote:
Two women, A and B working separately can mow a field in 8 and 12 hrs respectively. If they work together in stretches on 1 hr alternately, A beginning at 9:00 AM, when will the mowing be finished?

HI Bunnel
Please clarify me where I have gone wrong

Rate A-1/8
Rate B-1/12

let say A works for 4 hour and rate is 1/8 so total job done = 1/8*4=1/2
Similarly let say B works for 6 hour and rate is 1/12 so total job done=1/12*6=1/2

So both can finish the work in 10 hours if they work alternatively. 9.00 am+10 hour=19.00pm answer

Where i have gone wrong..............

Rgds
Prasannajeet

I think you misinterpreted the question. A and B work in shifts: A goes first and works for 1 hour, then goes B and works for 1 hour, ... Thus, for this scenario it's not possible A to work 4 hours and B 6 hours.

hey Bunuel,

thanks for the solution,

I just have one questions

if the rate came to 5/25 instead of 5/24, would the answer me 10 hours?

I stopped my solution at time = 24/5 = about 9.8 hours. Not sure what alerts us to solve further for the breakdown.
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Re: Two women, A and B working separately can mow a field in 8 [#permalink]

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09 Nov 2015, 22:02
let's assume that the total work is 48
the A will do in 1 hour 6 parts of the work, B will do 4 parts of the work
2 hours - 10 parts of the work
4 hours - 20 parts
6 hours - 30 parts
8 hours - 40 parts
9 hours - 46 parts
9.5 hours - 48 parts

started at 9AM + 9.5hr = 18:30
Re: Two women, A and B working separately can mow a field in 8   [#permalink] 09 Nov 2015, 22:02
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